Parallel -- both within the strips and between them -- would seem to make more sense. In that configuration you'd need a 3.2V supply which could provide up to 54*700 ma, or about 38 amps.

Note that this comes out to a bit over 120 watts. Not all of that will come out as light; some of it is going to be heat. You'd better think about how you're cooking this beast if you don't want to cook the LEDs.